Fundamental Methods of Mathematical Economics

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Description: It has been 20 years since the last edition of this classic text. Kevin Wainwright, a long time user of the text (British Columbia University and Simon Fraser University), has executed the perfect revision--he has updated examples, applications andMore...

It has been 20 years since the last edition of this classic text. Kevin Wainwright, a long time user of the text (British Columbia University and Simon Fraser University), has executed the perfect revision--he has updated examples, applications and theory without changing the elegant, precise presentation style of Alpha Chiang. Readers will find the wait was worthwhile.

Preface

Introduction

The Nature of Mathematical Economics

Mathematical versus Nonmathematical Economics

Mathematical Economics versus Econometrics

Economic Models

Ingredients of a Mathematical Model

The Real-Number System

The Concept of Sets

Relations and Functions

Types of Function

Functions of Two or More Independent Variables

Levels of Generality

Static (or Equilibrium) Analysis

Equilibrium Analysis in Economics

The Meaning of Equilibrium

Partial Market Equilibrium--A Linear Model

Partial Market Equilibrium--A Nonlinear Model

General Market Equilibrium

Equilibrium in National-Income Analysis

Linear Models and Matrix Algebra

Matrices and Vectors

Matrix Operations

Notes on Vector Operations

Commutative, Associative, and Distributive Laws

Identity Matrices and Null Matrices

Transposes and Inverses

Linear Models and Matrix Algebra (Continued)

Conditions for Nonsingularity of a Matrix

Test of Nonsingularity by Use of Determinant

Basic Properties of Determinants

Finding the Inverse Matrix

Cramer's Rule

Application to Market and National-Income Models

Leontief Input-Output Models

Limitations of Static Analysis

Comparative-Static Analysis

Comparative Statics and the Concept of Derivative

The Nature of Comparative Statics

Rate of Change and the Derivative

The Derivative and the Slope of a Curve

The Concept of Limit

Digression on Inequalities and Absolute Values

Limit Theorems

Continuity and Differentiability of a Function

Rules of Differentiation and Their Use in Comparative Statics

Rules of Differentiation for a Function of One Variable

Rules of Differentiation Involving Two or More Functions of the Same Variable

Rules of Differentiation Involving Functions of Different Variables

Partial Differentiation

Applications to Comparative-Static Analysis

Note on Jacobian Determinants

Comparative-Static Analysis of General-Function Models

Differentials

Total Differentials

Rules of Differentials

Total Derivatives

Derivatives of Implicit Functions

Comparative Statics of General-Function Models

Limitations of Comparative Statics

Optimization Problems

Optimization: A Special Variety of Equilibrium Analysis

Optimum Values and Extreme Values

Relative Maximum and Minimum: First-Derivative Test

Second and Higher Derivatives

Second-Derivative Test

Digression on Maclaurin and Taylor Series

Nth-Derivative Test for Relative Extremum of a Function of One Variable

Exponential and Logarithmic Functions

The Nature of Exponential Functions

Natural Exponential Functions and the Problem of Growth

Logarithms

Logarithmic Functions

Derivatives of Exponential and Logarithmic Functions

Optimal Timing

Further Applications of Exponential and Logarithmic Derivatives

The Case of More than One Choice Variable

The Differential Version of Optimization Conditions

Extreme Values of a Function of Two Variables

Quadratic Forms--An Excursion

Objective Functions with More than Two Variables

Second-Order Conditions in Relation to Concavity and Convexity

Economic Applications

Comparative-Static Aspects of Optimization

Optimization with Equality Constraints

Effects of a Constraint

Finding the Stationary Values

Second-Order Conditions

Quasiconcavity and Quasiconvexity

Utility Maximization and Consumer Demand

Homogeneous Functions

Least-Cost Combination of Inputs

Some Concluding Remarks

Dynamic Analysis

Economic Dynamics and Integral Calculus

Dynamics and Integration

Indefinite Integrals

Definite Integrals

Improper Integrals

Some Economic Applications of Integrals

Domar Growth Model

Continuous Time: First-Order Differential Equations

First-Order Linear Differential Equations with Constant Coefficient and Constant Term

Dynamics of Market Price

Variable Coefficient and Variable Term

Exact Differential Equations

Nonlinear Differential Equations of the First Order and First Degree

The Qualitative-Graphic Approach

Solow Growth Model

Higher-Order Differential Equations

Second-Order Linear Differential Equations with Constant Coefficients and Constant Term

Complex Numbers and Circular Functions

Analysis of the Complex-Root Case

A Market Model with Price Expectations

The Interaction of Inflation and Unemployment

Differential Equations with a Variable Term

Higher-Order Linear Differential Equations

Discrete Time: First-Order Difference Equations

Discrete Time, Differences, and Difference Equations

Solving a First-Order Difference Equation

The Dynamic Stability of Equilibrium

The Cobweb Model

A Market Model with Inventory

Nonlinear Difference Equations--The Qualitative-Graphic Approach

Higher-Order Difference Equations

Second-Order Linear Difference Equations with Constant Coefficients and Constant Term

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